Solve for x(t) and v(t) given a Force equation using Mathematica

  • #1
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Capture d’écran 2019-01-24 à 23.09.08.png

Homework Statement




Homework Equations


F= ma or F= md^2x/dt^2

The Attempt at a Solution


I know that this second order differential is non linear. I attempted to solve the problem as -k/x^2 = md^2x/dt^2 but I'm getting trouble since it is a second order ODE and I haven't learned how to solve those yet. I was also looking at my class notes to a similar problem but my professor included potential energy? I'm a bit confused. Any help would be greatly appreciated. If you can also show me how to solve this on Mathematica, that would also be a plus. I don't have any experience with it.
 

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Answers and Replies

  • #2
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update: i think i may have solved the first part? Now I need to figure out to put in on Mathematica.
IMG_3534.jpg
 

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  • #3
ZapperZ
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You need to use the chain rule from calculus.

You know that a = dv/dt.

However, this can also be written as a = (dv/dx) * (dx/dt) = v (dv/dx).

This means that your force equation a = F/m can now be written as

[tex]v \frac{dv}{dx} = \frac{F}{m}[/tex]

Consequently, what you need to solve (or integrate) is

[tex]v dv = \frac{F}{m} dx[/tex]

since F is given as a function of x.

Zz.
 

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